Publication Cover
Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 11
135
Views
13
CrossRef citations to date
0
Altmetric
Articles

Inverse problems for the stationary and pseudoparabolic equations of diffusion

&
Pages 1997-2010 | Received 28 Jan 2018, Accepted 07 Feb 2018, Published online: 25 Feb 2018

References

  • Lyubanova AS . Identification of a constant coefficient in an elliptic equation. Appl Anal. 2008;87:1121–1128.
  • Lyubanova AS . On an inverse problem for quasi-Linear elliptic equation. J Siberian Federal Univ Math Phys. 2015;8:38–48.
  • Lyubanova AS . The inverse problem for the nonlinear pseudoparabolic equation of filtration type. J Siberian Federal Univ Math Phys. 2017;10:4–15.
  • Lyubanova AS , Tani A . An inverse problem for pseudoparabolic equation of filtration: the existence, uniqueness and regularity. Appl Anal. 2011;90:1557–1571.
  • Prilepko AI , Orlovsky DG , Vasin IA . Methods for solving inverse problems in mathematical physics. New York (NY): Marcel Dekker; 2000.
  • Alekseev GV , Kalinina EA . Identification of the lowest coefficient of a stationary convection-diffusion-reaction equation. Sibirsk Zh Industr Mat. 2007;10:3–16. Russian.
  • Egger H , Pietschmann J-F , Schlottbom M . Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem. Inverse Prob. 2014;30:035009.
  • Rundell W . Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecified boundary data. Appl Anal. 1980;10:231–242.
  • Kozhanov AI . [On the solvability of the coefficient inverse problems for equations of Sobolev type]. Nauchniye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya Matematika Phizika. 2010;5:88–98. Russian.
  • Mamayusupov MS . The problem of determining coefficients of a pseudoparabolic equation. In: Studies in integro-differential equations. Vol. 16. Frunze: Ilim; 1983. p. 290–297. Russian.
  • Pyatkov SG , Shergin SN . On some mathematical models of filtration type. Bull South Ural State Univ Ser Math Model Program Comput Softw (Bulletin SUSU MMCS). 2015;8:105–116.
  • Bukhgeim AL , Klibanov MV . Global uniqueness of a class of multidimensional inverse problems. Soviet Math Dokl. 1981;24:244–247.
  • Klibanov MV . Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems. J Inverse Ill-Posed Probl. 2013;21:477–560.
  • Klibanov MV , Timonov A . Carleman estimates for coefficient inverse problems and numerical applications. Utrecht: VSP; 2004.
  • Mehraliyev YT , Kanca F . An inverse boundary value problem for a second order elliptic equation in a rectangle. Math Model Anal. 2004;19:241–256.
  • Solov’ev VV . Coefficient inverse problem for Poisson’s equation in a cylinder. Comput Math Math Phys. 2011;51:1738–1745.
  • Li T-T , White LW . Total flux (nonlocal) boundary value problems for pseudoparabolic equation. Appl Anal. 1983;16:17–31.
  • Ladyzenskaja OA , Uralceva NN . Linear and quasilinear elliptic equations. New York (NY): Academic Press; 1973; English transl. Moskva: Nauka; 1964.
  • Lions J-L , Magenes E . Problemes aux limites non homogenes et applications. Vol. 1. Paris: Dunod; 1968. (Travaux et recherches mathematiques; vol. 17).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.